from without to satisfy us that A is predicable of all [Greek: G]. The text, as translated by Boethius and others, escapes that particular incongruity, though in another way, but it introduces a version inadmissible on other grounds. Instead of [Greek: tô=| _dê\ G_ o(/lô| u(pa/rchei to\ A, pa=n ga\r to\ a)/cholon makro/bion], Boethius has [Greek: tô=| _dê\ B_ o(/lô| u(pa/rchei to\ A, pa=n ga\r to\ a)/cholon makro/bion]. This cannot be accepted, because it enunciates the conclusion of the syllogism as if it were one of the premisses. We must remember that the conclusion of the Aristotelian Syllogism from Induction is, that A is predicable of B, one of the premisses to prove it being that A is predicable of the minor term C. But obviously we cannot admit as one of the premisses the proposition that A may be predicated of B, since this proposition would then be used as premiss to prove itself as conclusion. If we examine the Aristotelian Inductive Syllogism which is intended to conduct us to the final _probandum_, we shall see that the terms of it are incorrectly set out by Bekker and Waitz, when they give the minor term [Greek: G] as designating [Greek: to\ kath' e(/kaston makro/bion]. This last is not one of the three terms, nor has it any place in the syllogism. The three terms are: 1. A--major--the class-term or class [Greek: makro/bion]--_longævum_. 2. B--middle--the class term or class [Greek: a)/cholon]--bile-less. 3. C--minor--the individual bile-less animals, man, horse, &c. There is no term in the syllogism corresponding to the individual _longæva_ or long-lived animals; this last (I repeat) has no place in the reasoning. We are noway concerned with the totality of long-lived animals; all that the syllogism undertakes to prove is, that in and among that totality all bile-less animals are included; whether there are or are not other long-lived animals besides the bile-less, the syllogism does not pretend to determine. The equation or co-extensiveness required (as described by M. Barthélemy St. Hilaire in his note) is not between the individual long-lived animals and the class, bile-less animals (middle term), but between the aggregate of individual animals known to be bile-less and the class, bile-less animals. The real minor term, therefore, is (not the individual _long-lived_ animals, but) the individual _bile-less_ animals. The two premisses of the Inductive Syllogism will stand thus:-- Men, Horses, Mules, &c., are long-lived (major). Men, Horses, Mules, &c., are bile-less (minor). And, inasmuch as the subject of the minor proposition is co-extensive with the predicate (which, if quantified according to Hamilton's phraseology, would be, _All_ bile-less animals), so that the proposition admits of being converted simply,--the middle term will become the subject of the conclusion, All bileless animals are long-lived.]